Divisibility Rule of 156
2026-02-28 19:02 Diff
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Last updated on August 5, 2025

The divisibility rule is a way to determine whether a number is divisible by another number without using the traditional division method. In real life, divisibility rules are useful for quick calculations, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 156.

What is the Divisibility Rule of 156?

The divisibility rule for 156 is a method to find out if a number is divisible by 156 without using the division method. Let's check whether 18720 is divisible by 156 using the divisibility rule.

Step 1: Check if the number is divisible by 3, 4, and 13, as 156 is the product of these numbers (3 × 4 × 13 = 156).

Step 2: For divisibility by 3, sum all the digits. If the sum is a multiple of 3, the number is divisible by 3. In 18720, the sum is 1 + 8 + 7 + 2 + 0 = 18, which is divisible by 3.

Step 3: For divisibility by 4, check the last two digits. If they form a number divisible by 4, then the entire number is divisible by 4. Here, 20 is divisible by 4.

Step 4: For divisibility by 13, use the rule where you take the last digit, multiply it by 9, and subtract from the rest of the number. If the result is divisible by 13, then the number is divisible by 13. Here, multiply 0 by 9 and subtract from 1872, giving 1872, which is divisible by 13.

Since 18720 is divisible by 3, 4, and 13, it is also divisible by 156.
 

Tips and Tricks for Divisibility Rule of 156

Learn the divisibility rule to help master division. Let's explore a few tips and tricks for the divisibility rule of 156.

  • Know the factors: Understand that 156 is the product of 3, 4, and 13. Check divisibility by these factors.
     
  • Sum of digits for 3: Remember, if the sum of a number's digits is a multiple of 3, the number is divisible by 3.
     
  • Last two digits for 4: Only the last two digits matter for divisibility by 4.
     
  • Special rule for 13: Multiply the last digit by 9 and subtract from the remaining number to check for divisibility by 13.
     
  • Verify with division: Use the division method to confirm and cross-check results.
     

Common Mistakes and How to Avoid Them in Divisibility Rule of 156

The divisibility rule of 156 helps us quickly check if a number is divisible by 156, but common mistakes like calculation errors can lead to incorrect results. Here, we will address some common mistakes and their solutions.

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Problem 1

Is 1872 divisible by 156?

Okay, lets begin

Yes, 1872 is divisible by 156.

Explanation

To check if 1872 is divisible by 156, we need to follow these steps:


1) Check if the number is divisible by 3. The sum of the digits (1 + 8 + 7 + 2 = 18) is divisible by 3.


2) Check if the number is divisible by 4. The last two digits, 72, are divisible by 4.


3) Check if the number is divisible by 13. Subtract 9 times the last digit from the rest of the number: 187 - (9 x 2) = 169, which is divisible by 13.


Since 1872 meets all these conditions, it is divisible by 156.

Well explained 👍

Problem 2

Check if 2496 is divisible by 156.

Okay, lets begin

Yes, 2496 is divisible by 156.

Explanation

To verify the divisibility of 2496 by 156:


1) Check divisibility by 3: The sum of digits (2 + 4 + 9 + 6 = 21) is divisible by 3.


2) Check divisibility by 4: The last two digits, 96, are divisible by 4.


3) Check divisibility by 13: Subtract 9 times the last digit from the rest: 249 - (9 x 6) = 195, which is divisible by 13.

Since all conditions are satisfied, 2496 is divisible by 156.

Well explained 👍

Problem 3

Is 312 divisible by 156?

Okay, lets begin

Yes, 312 is divisible by 156.

Explanation

To determine if 312 is divisible by 156:


1) Check divisibility by 3: The sum of digits (3 + 1 + 2 = 6) is divisible by 3.


2) Check divisibility by 4: The last two digits, 12, are divisible by 4.


3) Check divisibility by 13: Subtract 9 times the last digit from the rest of the number: 31 - (9 x 2) = 13, which is divisible by 13.


Hence, 312 is divisible by 156.

Well explained 👍

Problem 4

Can 429 be divisible by 156?

Okay, lets begin

No, 429 is not divisible by 156.
 

Explanation

To check if 429 is divisible by 156:


1) Check divisibility by 3: The sum of digits (4 + 2 + 9 = 15) is divisible by 3.


2) Check divisibility by 4: The last two digits, 29, are not divisible by 4.


3) Even if we checked for divisibility by 13, the failure of divisibility by 4 is enough to conclude that 429 is not divisible by 156.
 

Well explained 👍

Problem 5

Is 624 divisible by 156?

Okay, lets begin

Yes, 624 is divisible by 156.

Explanation

To verify the divisibility of 624 by 156:


1) Check divisibility by 3: The sum of digits (6 + 2 + 4 = 12) is divisible by 3.


2) Check divisibility by 4: The last two digits, 24, are divisible by 4.


3) Check divisibility by 13: Subtract 9 times the last digit from the rest: 62 - (9 x 4) = 26, which is divisible by 13.
Thus, 624 is divisible by 156.

Well explained 👍

FAQs on Divisibility Rule of 156

1. What is the divisibility rule for 156?

Check if a number is divisible by 3, 4, and 13. If it is divisible by these numbers, it is divisible by 156.
 

2.How many numbers between 1 and 1000 are divisible by 156?

There are 6 numbers between 1 and 1000 divisible by 156: 156, 312, 468, 624, 780, and 936.
 

3. Is 624 divisible by 156?

Yes, because 624 is divisible by 3, 4, and 13

4.What if I get 0 after subtraction in the step for 13?

If you get 0, it means the number is divisible by 13.

5. Does the divisibility rule of 156 apply to all integers?

Yes, the divisibility rule of 156 applies to all integers.
 

Important Glossaries for Divisibility Rule of 156

  • Divisibility rule: A set of guidelines used to determine if one number is divisible by another without performing division.
     
  • Factors: Numbers that multiply together to form another number. For 156, the factors are 3, 4, and 13.
     
  • Multiples: The result of multiplying a number by an integer. For example, multiples of 156 include 156, 312, etc.
     
  • Sum of digits: The total obtained by adding all the digits of a number, used to check divisibility by 3.
     
  • Subtraction: The process of taking one number away from another, used in the rule for divisibility by 13.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.